Two travelers set out at the same time to travel opposite ways round a circular railway. Trains start each way every fifteen minutes: on the hour, fifteen minutes past, half past, and forty-five minutes past. Clockwise trains take two hours for the journey, counterclockwise trains take three hours.
Including trains seen at the starting point and the ones they are traveling on, how many trains did each traveler see on his journey?
(In reply to Sanity check (spoiler)
by Steve Herman)
..."Charlie has shown that this number is 20..."
Each traveler covers span of 5 hrs, i.e. 5/.25=20 intervals.
A fence of 20 segments needs 21 posts.
Circulating traveler during his full round meets 21 trains.
If he were to continue endlessly then we may agree upon the number 20 per round, since the last meeting of round k would be counted as belonging to round k+1.
If the traveler descended his train after n full rounds, and the crazy schedule still went on he might have recorded 20*n+1 encounters.
Of course that does not include the train that carried him (1 should be added per KS's instructions).
I believe al of us endorse the above results.
If not, show me where I have erred.